Reference: Cosmology at the millennium, Michael S. Turner and J. Anthony Tyson, in
                  "Reviews of Modern Physics", 71 (1999) S145

                  Cosmic microwave background radiation , Lyman Page and David Wilkinson, in
                  "Reviews of Modern Physics", 71 (1999) S173

               Essential Relativity , Wolfgang Rindler, Springer-Verlag, 1977

There are several observations that lend support to the "Standard Model" of Cosmology. This is called the "Big Bang" Theory. We will discuss a few of these critical data.

1) The expansion of the universe as seen by galactic redshifts
2) The cosmic microwave background
3) The abundance of the light elements below lithium

1) Cosmological Redshift
Evidence for a pattern to galactic motion began accumulating by Slipher, Hubble, Humason in the early years of the 20th century that galaxies were moving apart . These determinations were done using the shift in spectral lines between the distant source and a laboratory source.

When we look at spectral shifts of galaxies there are two causes for these shifts we must keep in mind when trying to interpret them.

i) Doppler shift - caused by the motion through space of the object , could be red or blue shifted
 

ii) redshift -  Galaxies on the whole are largely moving apart, although there may be some local differences where they orbit about each other due to mutual gravitational attraction. The large scale motion is caused by the expansion of space itself. Here the scale factor of space is changing in time so that not only the galaxies are being carried farther apart, but also the wave  length of electromagnetic radiation is being stretched. This expansion is sometimes referred to as the "Hubble flow". Astronomers use the notation "z" to indicate the fractional change of the wave length. The ratio of wave lengths(l(t) is wave length) at two separate times t₁ and t₂ depends on the "scale factor", or radius R(t) of the universe in a certain model.

  1 + z = l(t₁)/l(t₂) = R(t₁)/R(t₂).   Red shift formula

The expansion, or contraction, of the universe is an inevitable consequence of General Relativity, proposed by Albert Einstein at the beginning  of the 20th century.  Einstein effectively took the "Action at a Distance" theory of Newton, and incorporated gravitational effects into the geometry of space-time.

A Comparison of the Newtonian and Einsteinian Views on Space-Time and Gravitational Dynamics

	Newton	Einstein
time	absolute and universal	connected to space
space	absolute, flat, an arena for events to take place	In conjunction with time, space is "distorted" by the presence of mass. The distortion of space-time can be determined by solving Einstein's "Field equations"
dynamics	caused by "forces" acting at a distance between bodies	Bodies with mass follow "geodesics" in  space-time, which are intervals of  extremal lengths. Photons(light) follow geodesics whose interval length is zero.

The solutions of General Relativity which are associated with this dynamic picture of the universe were proposed by Friedmann, Lemaitre, Robertson, and Walker. Einstein himself had originally conceived of a model to describe a static universe, which is not what is observed.

The Hubble constant is a measure of the expansion  rate of the universe.  Hubble's original value of
550 km/sec/Mpc has been revised several times in subsequent measurements. The best value today seems to be 70 km/s/Mpc.

2) Cosmic Microwave Background
 The picture we have of the Big Bang is one of a Universe at some initial time that was extremely dense and hot. If we follow the solutions of General Relativity backwards in time we are led unavoidably to such a conclusion. The Universe is far from a static place. Evolution is the rule for the Cosmos. Modern particle physics gives us the hope of being able to calculate back in time to about 10^-43 seconds. At these times near the creation of our observable universe the conditions were one of a "soup" of particles and anti-particles and photons ( the particles of light ). The physics problem at early times is actually easier than at latter times because the Universe looked like the inside of a hot oven. From thermodynamics we can calculate the relative abundances of the elementary particles. The BB theory predicts that about 380,000 years after the creation of the universe the temperature had cooled sufficiently, to about 4000K, that neutral atoms could be formed. The photons present at that time would then have a much reduced probability of scattering from neutral atoms as compared to free electrons and protons. We say that the radiation "decoupled" from the matter then. Decoupling Event

If we look at the "photon gas" that existed at the time of this decoupling we should be able to see a Black Body spectrum characteristic of a temperature of about 4000K. However, from the theory of General Relativity this radiation will also suffer a red-shift, just like the radiation emitted from receding galaxies. Thus when we look at that event ( the universe at the decoupling of matter and radiation) we see a Black Body spectrum that has been shifted in temperature by a factor of over 1000. This also means that the universe is this same factor bigger ( about 1000 ) now than it was then. The temperature T(t) also scales with the radius of the universe, but in the inverse way from the wave length.

            T(t₁)/T(t₂) = R(t₂)/R(t₁).  scaling of Black Body temperature with "radius" of the Universe.

This relationship of the Black Body spectrum temperature with red-shift is seen through out the the times that we look back. When we see a galaxy with a particular red-shift we can calculate what the Black Body temperature should be. Then when we look at the excitation of certain atomic states in Carbon we find the right number of excited Carbon atoms corresponding to the "thermal photon bath" in which they sit.

The microwave background was predicted in 1948 by Gamow et al. as a consequence of the Big Bang. In the mid 1960's it was observed by Penzias and Wilson at Bell Labs, serendipitously, while they were trying to locate the source of "noise" in their microwave receivers. The temperature of the microwave background is 2.7277K. It is very nearly isotropic, as you might expect looking into the mouth of an oven. There is a tiny anisotropy, nevertheless, which turns out to be of fundamental importance in the description of how galaxies formed.COBE spectrum

3) Abundance of the light elements below lithium

Consider the table of chemical elements. Where did these elemements come from? Well before the matter and radiation decoupled at t=380000 years, the Universe formed its present supply of the light elements, notably hydrogen, deuterium, helium, and lithium(Recent WMAP results show a significant theory problem.). This occurred over a period from about 3 minutes to 15 minutes after the Big Bang event when the Universe's temperature was about 10⁹K, or equivalently about 300 million times smaller in size. At these temperatures the protons and neutrons could join to build up the elements stated above. Because of the strong electrical repulsion between like charges protons and protons will generally stay so far away from each other that nuclear reactions ( actually the weak interaction in the proton-proton case) will be strongly suppressed. It is only at sufficiently high temperatures, such as those found in the early universe or in the cores of stars, that the nuclei have enough energy to overcome the electrical repulsion and that nuclear fusion can occur. Since the the Universe was expanding rapidly it did not linger in this high temperature regime long enough for heavier elements to be formed. The heavier elements, above lithium, would not be formed until stars started to form them in stellar nucleosynthesis. The predictions from BB theory are that 75% of the ordinary mass of the Universe should be in the form of protons and about 25% of the ordinary mass should be in the form of helium. Nucleosynthesis(pdf)